Iterative focused millimeter wave integrated communication and sensing method

ABSTRACT

Provided is an iterative focused millimeter wave integrated communication and sensing method, which converts an environmental sensing problem into a compressed sensing reconstruction problem, and realizes the initial coarse sensing of the environment based on an approximate message passing algorithm; according to a background determining method, the present disclosure divides and determines a target object, removes the influence of background scatters on a receiving signal, and removes the background scatters repeatedly and iteratively, so as to obtain a more accurate focus sensing result of the target object. Compared with existing environment sensing reconstruction algorithms, the iterative focused millimeter wave environment sensing algorithm of the present disclosure significantly improves the accuracy of environment sensing, solves the problem that a large-scale environment cannot be accurately sensed due to limited system resources, and provides an efficient environment sensing method for the future design of integrated sensing and communication systems.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a continuation of International Application No. PCT/CN2022/138958, filed on Dec. 14, 2022, which claims priority to Chinese Application No. 202210906702.0, filed on Jul. 29, 2022, the contents of both of which are incorporated herein by reference in their entireties.

TECHNICAL FIELD

The present disclosure belongs to the technical field of wireless communication, and particularly relates to an iterative focused millimeter wave integrated communication and sensing method.

BACKGROUND

In the current wireless communication field, the emergence of innovative wireless communication technologies, such as ultra-large-scale multiple-input multiple-output (MIMO) technology, intelligent reflecting surface (IRS) and wireless artificial intelligence (AI), provides more possibilities for the design of future wireless communication systems. In the foreseeable future wireless communication present disclosure scenarios, technologies such as autonomous driving, intelligent robot navigation and unmanned aerial vehicle control need not only wireless broadband connection, but also accurate environmental information, including the position, shape and electromagnetic characteristics of objects in the environment. Therefore, as the research hotspot of the 6th generation (6G) wireless communication system, the integrated sensing and communication (ISAC) technology aims to realize environmental sensing by using wireless communication equipment and infrastructure.

In an uplink wireless communication scenario, users send communication signals to the base station for reception, and the transmitted signals are reflected and scattered by objects in the environment, such that the receiving signals of the base station contain environmental information. The design of the integrated system of sensing and communication has a great difficulty: how to deal with a large number of potential unknown variables in the environment, therefore the sparsity of the target environment itself shall be utilized. For example, in the urban wireless communication scene, buildings are sparsely distributed in the block. In addition, in the wireless communication application scenario, electromagnetic waves spread widely, and any environmental scatterer covered by wireless signals will affect the propagation of electromagnetic waves. However, the resources available for environmental sensing, such as the number of users, the number of base station receiving antennas and the number of subcarriers, are limited. Even taking advantage of the sparsity of environmental information, environmental sensing still faces the problem of large system resource expenditure caused by a large number of environmental information variables. At present, the existing integration method of millimeter wave communication and sensing does not take into account the influence of limited system resources on sensing algorithms. Under the condition of limited system resources, only a coarse sensing of the environment can be achieved, and fuzzy imaging results can be obtained. It is urgent to focus on specific targets with limited resources, so as to obtain accurate environmental sensing results. To sum up, how to use limited system resources to achieve accurate sensing of specific targets has high research difficulty and practical significance.

SUMMARY

In view of the shortcomings of the prior art, the object of the present disclosure is to realize environment sensing by a base station using uplink data sent by multiple users in an uplink wireless communication scenario. The present disclosure uses the pilot signal of the existing communication system or other known data sequences for sensing, and can be compatible with the existing communication system to realize the integration of sensing and communication. Considering that the system resources used for sensing are limited, it is impossible to sense all the environment in a large range, an iterative focused millimeter wave environment sensing method for specific targets is proposed.

The object of the present disclosure is achieved by the following technical solution:

Provided is an iterative focused millimeter wave integrated communication and sensing method. In an uplink wireless communication scenario, active users send communication signals to the base station for reception, and the sent signals are transmitted to the base station via multipath channel. The method includes the following steps:

S1, in any time slot, receiving, by a base station, pilot frequency sequence signals with a certain length sent by all active users in an environment to obtain receiving signals, wherein the receiving signals are signals after the pilot frequency sequence signals are influenced by the environment.

S2, converting an environmental sensing problem of a specific target into a compressed sensing reconstruction problem by using the receiving signals in the step S1 based on a multi-beam multi-carrier millimeter wave channel model.

S3, solving the compressed sensing reconstruction problem in step S2 based on an approximate message passing method to obtain a coarse initial result of environment sensing.

S4, selecting a predetermined region as a focused region of interest from the whole environment based on the coarse initial result of environmental sensing, and dividing and determining an target object in the region of interest according to a background determining method and removing the influence of background scatters outside the region of interest on the receiving signals to obtain receiving signals corresponding to the target object.

S5, calculating an environmental sensing result based on the receiving signals corresponding to the target object obtained in the step S4.

S6, repeating step S4 and step S5 in sequence until the algorithm convergence to obtain a final environment sensing result.

Further the step S2 specifically includes the following steps:

S21, discretizing environmental information in the receiving signals in step S1 into pixels; here, each pixel represents environmental information in a small square with a surrounding size of l_(s)×w_(s), and if an environmental size of a whole range is L_(s)×W_(s), a total number of the pixels is N_(s)=L/l_(s)×W/w_(s); an interior of each pixel may be empty, or there may be scatters; a scattering coefficient x_(n) _(s) , is used to represent the scattering coefficient of a small cube where a n_(s) ^(th) point cloud is located; if an interior of the small cube is empty, then x_(n) _(s) =0; therefore, the environmental information of a whole room can be expressed as x=[x₁, x₂, . . . , x_(N) _(s) ]^(T).

S22, using a multi-beam multi-carrier millimeter wave channel model, wherein at an n_(f) ^(th) subcarrier frequency, the receiving signals received by a receiving antenna of the base station are expressed as follows:

y _(n) _(f) =w _(n) _(f) (H _(n) _(f) ^(s→B)diag(δx)H _(n) _(f) ^(u→s) +H _(n) _(f) ^(LOS))s _(n) _(f) +n=w _(n) _(f) (H _(n) _(f) ^(NLOS) +H _(n) _(f) ^(LOS))s _(n) _(f) +n

where y_(n) _(f) ε

^(N) ^(c) ^(xK) represents the receiving signals with a length of K code elements of RF links of N_(c) base stations, w_(n) _(f) ε

^(N) ^(c) ^(xN) ^(R) is a beam forming vector of N_(R) uniform linear array receiving antennas of the base stations, δ is a normalized coefficient of a scattering coefficient, which is selected according to a pixel size l_(s)×w_(s) and describes the physical relationship between an electromagnetic wave receiving region and a receiving power s_(n) _(f) ε

^(N) ^(u) ^(xK) represents pilot frequencies with a length of K code elements sent by N_(u) users, n is noise; H_(n) _(f) ^(LOS) represents a free-space propagation channel from N_(u) users to N_(R) receiving antennas at an n_(f) ^(th) subcarrier frequency; H_(n) _(f) ^(NLOS) is a Non-Line-of-Sight (NLOS) channel on a n_(f) ^(th) subcarrier;

H_(n) _(f) ^(LOS) is expressed as

H _(n) _(f) ^(LOS) =e _(n) _(f) ^(LOS) G _(n) _(f) ^(LOS)

where e_(n) _(f) ^(LOS) is a steering vector of N_(u) users and G_(n) _(f) ^(LOS) is a channel gain from N_(u) users to the base station;

${e_{n_{f}}^{LOS}\left( {n_{R},n_{u}} \right)} = {e^{j\frac{2\pi}{\lambda_{n_{f}}}{({n_{R} - 1})}{dsin}\theta_{n_{u}}^{LOS}}/\sqrt{N_{R}}}$

where j represents a complex code element, n_(R) is a serial number of the receiving antenna, θ_(n) _(u) ^(LOS) is an arrival angle of a n_(u) ^(th) user, and d is a uniform linear array antenna spacing deployed by the base station, λ_(n) _(f) is a wavelength; G_(n) _(f) ^(LOS) is expressed as follows:

G_(n_(f))^(LOS) = diag([g_(n_(f), 1)^(LOS)e^(jφ_(n_(f), 1)^(LOS)), …, g_(n_(f), N_(u))^(LOS)e^(jφ_(n_(f), N_(u))^(LOS))])

where g_(n) _(f) ^(n) _(u) ^(LOS) and φ_(n) _(f) ^(n) _(u) ^(LOS) are a channel amplitude gain and a phase shift from the n_(u) ^(th) user to the base station, respectively.

At the n_(f) ^(th) subcarrier frequency, a free-space propagation channel H_(n) _(f) ^(u→s)(n_(s), n_(u)) from the n_(u) ^(th) user to a n_(s) ^(th) pixel is expressed as:

H_(n_(f))^(u → s)(n_(s), n_(u)) = g_(n_(f))^(u → s)(n_(s), n_(u))e^(jφ_(n_(f))^(u → s)(n_(s), n_(u)))

where g_(n) _(f) ^(u→s)(n_(s), n_(u)) and φ_(n) _(f) ^(u→s)(n_(s), n_(u)) are a channel amplitude gain and a phase shift from n_(u) ^(th) user to the n_(s) ^(th) pixel, respectively.

At the n_(f) ^(th) subcarrier frequency, a free-space propagation channel H_(n) _(f) ^(s→B)∈

^(N) ^(R) ^(xN) _(s) from N_(s) pixels to N_(R) receiving antennas is expressed as:

H _(n) _(f) ^(s→B) =e _(n) _(f) ^(s→B) G _(n) _(f) ^(s→B)

where e_(n) _(f) ^(s→B) is a steering vector of N_(s) pixels and G_(n) _(f) ^(s→B) is a channel gain from N_(s) pixels to the base station;

${e_{n_{f}}^{s\rightarrow B}\left( {n_{R},n_{s}} \right)} = {e^{j\frac{2\pi}{\lambda_{n_{f}}}{({n_{R} - 1})}{dsin}\theta_{n_{s}}^{s\rightarrow B}}/\sqrt{N_{R}}}$

where n_(R) is a receiving antenna number, θ_(n) _(s) ^(s→B) an arrival angle of the n_(s) ^(th) pixel, and G_(n) _(f) ^(s→B) is expressed as follows:

G_(n_(f))^(s → B) = diag([g_(n_(f), 1)^(s → B)e^(jφ_(n_(f), 1)^(s → B)), …, g_(n_(f), N_(s))^(s → B)e^(jφ_(n_(f), N_(s))^(s → B))])

where g_(n) _(f) ^(n) _(s) ^(s→b) and φ_(n) _(f) ^(n) _(s) ^(s→b) are a channel amplitude gain and a phase shift from the n_(s) ^(th) pixel to the base station, respectively.

S23, expressing an estimation result of the environmental information as {circumflex over (X)}, which is expressed as follows:

{circumflex over (x)}=argmin_(x) _(ROI) ||X|| ₀ s.t.||y−w(H ^(LOS) +H ^(LOS))s|| ₂≤ε

where y is a receiving signal of all subcarriers, w is a beam forming vector of the uniform linear array receiving antenna of all subcarriers, x_(ROI) is environmental information in a region of interest, H^(NLOS) is a NLOS channel of all subcarriers, H^(LOS) is a LOS channel of all subcarriers, s is a transmitted signal of the NLOS channel of all subcarriers, and ε is a relaxation variable.

Since a free-space channel coefficient of a direct-view channel can be estimated by a numerical model, at the n_(f) ^(th) subcarrier frequency, part of the receiving signal {tilde over (y)}_(n) _(f) containing unknown environmental information is expressed as follows:

{tilde over (y)} _(n) _(f) =w _(n) _(f) H _(n) _(f) ^(s→B)diag(δx)H _(n) _(f) ^(u→s) s _(n) _(f) +n

By combining data of N_(f) subcarriers, an iterative focused environmental sensing problem of a specific target is converted into a compressed sensing reconstruction problem equation as follows:

$\begin{bmatrix} {{\overset{\sim}{y}}_{1}\left( {:,1} \right)} \\  \vdots \\ {{\overset{\sim}{y}}_{1}\left( {:,K} \right)} \\  \vdots \\ {{\overset{\sim}{y}}_{N_{f}}\left( {:,1} \right)} \\  \vdots \\ {{\overset{\sim}{y}}_{N_{f}}\left( {:,K} \right)} \end{bmatrix}_{N_{c}N_{f}K \times 1} = {\left. {{{\delta\begin{bmatrix} {w_{1}H_{1}^{s\rightarrow B}{{diag}\left( {H_{1}^{u\rightarrow s}{s_{1}\left( {:,1} \right)}} \right)}} \\  \vdots \\ {w_{1}H_{1}^{s\rightarrow B}{{diag}\left( {H_{1}^{u\rightarrow s}{s_{1}\left( {:,K} \right)}} \right)}} \\  \vdots \\ {w_{N_{f}}H_{N_{f}}^{s\rightarrow B}{{diag}\left( {H_{N_{f}}^{u\rightarrow s}{s_{N_{f}}\left( {:,1} \right)}} \right)}} \\  \vdots \\ {w_{N_{f}}H_{N_{f}}^{s\rightarrow B}{{diag}\left( {H_{N_{f}}^{u\rightarrow s}{s_{N_{f}}\left( {:,K} \right)}} \right)}} \end{bmatrix}}_{N_{c}N_{f}K \times N_{s}}\lbrack x\rbrack}_{N_{s} \times 1} + n}\Rightarrow\overset{\sim}{y} \right. = {{Ax} + {n.}}}$

Further, the step S3 specifically includes the following steps:

S31, firstly setting an initial coarse environmental sensing prior probability, and letting the environmental information be a Bernoulli-Gaussian distribution, wherein a probability density function p_(x)(x|q) is expressed as:

p _(x)(x|q)=(1−λ)δ(x)+λN(x|θ ^(x),σ^(x))

where x represents an element in the environmental information x, all parameters are expressed as q

[λ,θ^(x), σ^(x)], δ(·) is an impulse function, λ is a sparse coefficient; θ^(x)∈[0,1] and σ^(x) are a mean value and a variance of environmental information distribution, respectively, and N( represents a standard normal distribution;

S32, initializing approximate message passing algorithm parameters, and letting input functions g_(in)(·), g′_(in) (·) and output functions g_(out)(·), g′_(out)(·) be the following respectively

${{g_{in}\left( {\hat{v},\sigma^{v},q} \right)} = {\arg\max\limits_{x}{F_{in}\left( {x,\hat{v},\sigma^{v},q} \right)}}}{{F_{in}\left( {x,\hat{v},\sigma^{v},q} \right)} = {{\log{p_{x}\left( {x❘q} \right)}} - {\frac{1}{2\sigma^{v}}\left( {\hat{v} - x} \right)^{2}}}}{{g_{in}^{\prime}\left( {\hat{v},\sigma^{v},q} \right)} = \frac{1}{1 - {\sigma^{v}{\frac{\partial^{2}}{\partial x^{2}}{\log\left\lbrack {p_{x}\left( {x❘q} \right)} \right\rbrack}}}}}{{g_{out}\left( {y,\hat{p},\sigma^{z}} \right)} = \frac{y - \hat{p}}{\sigma^{w} + \sigma^{z}}}{{g_{out}^{\prime}\left( {y,\hat{p},\sigma^{z}} \right)} = {- \frac{1}{\sigma^{w} + \sigma^{z}}}}$

where, {circumflex over (v)}, σ^(v), {circumflex over (p)}, σ^(z) are input variables and σ^(w) is a noise variance;

let a number of iterations t_(G)=0, a residual ŝ(−1)=0, a sparse vector estimated mean value {circumflex over (x)}_(n) _(s) (t_(G))>0, and a sparse vector estimated variance σ_(n) _(s) (t_(G))>0;

S33, letting M=N_(c)N_(f)K, where N_(c) is a number of base stations, a is a number of code elements, N_(f) is a number of subcarriers; for m=1,2, . . . , M, calculating estimated mean value {circumflex over (z)}_(m)(t_(G)) and variance σ_(m) ^(z)(t_(G)) of a variable z_(m):

σ_(m) ^(z)(t _(G))=Σ_(n) _(s) A _(m,n) _(s) ²σ_(n) _(s) ^(x)(t _(G))

{circumflex over (p)}m(t _(G))=Σ_(n) _(s) A _(m,n) _(s) (t _(G))−σ_(m) ^(z)(t)ŝ _(m)(t _(G)−1)

{circumflex over (z)} _(m)(t _(G))=Σ_(n) _(s) A _(m,n) _(s) {circumflex over (x)} _(n) _(s) (t _(G))

S34, for m=1,2, . . . , M, calculating a mean value ŝ_(m)(t_(G)) and a variance σ_(m) ^(s)(t_(G)) of the residual:

ŝ _(m)(t _(G))=g _(out)(t _(G) , y _(m) , {circumflex over (p)} _(m)(t _(G)), σ_(m) ^(z)(t _(G)))

σ_(m) ^(s)(t _(G))=−g′ _(out)(t _(G) , y _(m) , {circumflex over (p)} _(m)(t _(G)), σ_(m) ^(z)(t _(G)))

where y_(m) is the m^(th) element of the receiving signal;

S35, for n_(s)=1,2, . . . , N_(s), calculating observed mean value {circumflex over (v)}_(n) _(s) (t _(G)) and variance σ_(n) _(s) ^(v)(t_(G)) of {circumflex over (x)}_(n) _(s) (t_(G)):

{circumflex over (v)} _(n) _(s) (t _(G))={circumflex over (x)} _(n) _(s) (t _(G))+σ_(n) _(s) ^(v)(t _(G))Σ_(m) A _(m,n) _(s) ŝ _(m)(t _(G))

σ_(n) _(s) (t _(G))=[Σ_(n) _(s) A _(m,n) _(s) ²σ_(n) _(s) ^(s)(t _(G))]⁻¹

S36, for n_(s)=1,2, . . . , N_(s), calculating observed mean value {circumflex over (x)}_(n) _(s) (t_(G)+1) and variance σ_(n) _(s) ^(x)(t_(G)+1) of x_(n) _(s) :

{circumflex over (x)} _(n) _(s) (t _(G)+1)=g _(in)(t _(G) , {circumflex over (v)} _(n) _(s) (t _(G)), σ_(n) _(s) ^(v)(t _(G)), q)

σ_(n) _(s) ^(x)(_(G)+1)=σ_(n) _(s) ^(v)(t _(G))g′ _(in)(t _(G) , {circumflex over (v)} _(n) _(s) (t _(G)), σ_(n) _(s) ^(r)(t _(g)), q)

S37, executing step S33 to step S36 repeatedly until a convergence condition Σ_(m)|y_(m)−{circumflex over (z)}_(m)(t_(G))|>ε_(G) is satisfied, where ε_(G) is an error tolerance;

S38, taking a sparse variable {circumflex over (x)}_(n) _(s) (t_(G)) as a coarse environmental sensing initial result of the environmental information x.

Further, the step S4 specifically incudes the following steps:

S41, selecting a predetermined region as a focused region of interest from the whole environment according to the coarse environmental sensing initial result and actual needs, wherein the target object is in the region of interest;

S42, in an ith iteration, detecting a background scatterer {circumflex over (x)}_(back) ^((i))(n_(s)) outside the region of interest as follows:

${{\hat{x}}_{back}^{(i)}\left( n_{s} \right)} = \left\{ \begin{matrix} {0,} & {{{\hat{x}}^{(i)}\left( n_{s} \right)} \leq {\gamma_{i}{or}{{\hat{x}}^{(i)}\left( n_{s} \right)}{inside}{{ROI}.}}} \\ {{{\hat{x}}^{(i)}\left( n_{s} \right)},} & {{{\hat{x}}^{(i)}\left( n_{s} \right)} \geq \gamma_{i}} \end{matrix} \right.$

where {circumflex over (x)}^((i))(n_(s)) represents a result in the ith iteration, y_(i) is a detection threshold of the background scatterer, and the detection threshold y_(i) shall decrease with the increase of the number of iterations;

S43, removing a background scattering part from the receiving signal to obtain a receiving signal ŷ_(ROI) ^((i+1)) of the target object in a region of interest (ROI) of an i+1^(st) iteration:

ŷ _(ROI) ^((i+1))=(1+a){tilde over (y)}+a(ŷ _(ROI) ^((i)) −Ax _(back) ^((i)))

where a is a weight variable, which is used to enhance the robustness of iterative algorithm, and the weight variable a should increase with the increase of the number of iterations.

Further, the step S5 specifically incudes the following steps:

S51, setting the prior probability of the environmental information in an iterative focused process, wherein in the i^(th) iteration, it is assumed that the background scatterer obeys Bernoulli Gaussian distribution, and a prior probability formula p(x_(back)) is as follows:

p(x _(back))=(1−λ)δ(x _(back))+δ

(x _(back); θ_(back,i), σ_(back))

where θ_(back,i) and σ_(back) represent the mean value and the variance of the background environmental information distribution, respectively, λ is a sparse coefficient, N(·) represents a standard normal distribution and x_(back) represents the background scatterer.

The scatterer distribution in the selected ROI is a Gaussian distribution, and there is no sparsity.

p(x _(ROI))=

(x _(ROI); θ_(ROI), σ_(ROI))

where θ_(ROI) and σ_(ROI) represent the mean value and variance of ROI environmental information distribution, respectively;

S52, according to the prior probability formula obtained in step S51, setting the prior probability p(x) of environmental information inside and outside the region of interest in the current i+1^(st) iteration, x={x_(ROI), x_(back)};

S53, initializing the approximate message passing algorithm parameters, and letting the input functions g_(in)(·), g′_(in)(·) and the output functions g_(out)(·), g′_(out)(·) be as follows:

${{g_{in}\left( {\hat{v},\sigma^{v},q} \right)} = {\arg\max\limits_{x}{F_{in}\left( {x,\hat{v},\sigma^{v},q} \right)}}}{{F_{in}\left( {x,\hat{v},\sigma^{v},q} \right)} = {{\log{p_{x}\left( {x❘q} \right)}} - {\frac{1}{2\sigma^{v}}\left( {\hat{v} - x} \right)^{2}}}}{{g_{in}^{\prime}\left( {\hat{v},\sigma^{v},q} \right)} = \frac{1}{1 - {\sigma^{v}{\frac{\partial^{2}}{\partial x^{2}}{\log\left\lbrack {p_{x}\left( {x❘q} \right)} \right\rbrack}}}}}{{g_{out}\left( {y,\hat{p},\sigma^{z}} \right)} = \frac{y - \hat{p}}{\sigma^{w} + \sigma^{z}}}{{g_{out}^{\prime}\left( {y,\hat{p},\sigma^{z}} \right)} = {- \frac{1}{\sigma^{w} + \sigma^{z}}}}$

Let the number of iterations t_(G)=0, the residual ŝ(−1)=0, the sparse vector estimated mean value {circumflex over (x)}_(n) _(s) (t_(G))>0 and the sparse vector estimate variance σ_(n) _(s) ^(x)(t_(G))>0;

S54, letting M=N_(c)N_(f)K, and for m=1,2, . . . , M, calculating estimated mean value {circumflex over (z)}_(m)(t_(G)) and variance σ_(m) ^(z)(t_(G)) of z_(m), which is specifically as follows:

σ_(m)(t _(G))=Σ_(n) _(s) A _(m,n) _(s) ²σ_(n) _(s) ^(x)(t _(G))

{circumflex over (p)} _(m)(t _(G))=Σ_(n) _(s) A _(m,n) _(s) {circumflex over (x)} _(n) _(s) (t _(G))−σ_(m) ^(z)(t)ŝ _(m)(t _(G)−1)

{circumflex over (z)} _(m)(t _(G))=Σ_(n) _(s) A _(m,n) _(s) {circumflex over (x)} _(n) _(s) (t _(G))

S55, for m=1,2, . . . , M, calculating a mean value ŝ_(m)(t_(G)) and a variance σ_(m) ^(s)(t_(G)) of the residual, which is specifically as follows:

ŝ _(m)(t _(G))=g _(out)(t _(G) , ŷ _(ROI,m) ^((i+1)) , {circumflex over (p)} _(m)(t _(G)), σ_(m) ^(z)(t _(G)))

σ_(m) ^(s)(t _(G))=−g′ _(out)(t _(G) , ŷ _(ROI,m) ^((i+1)) , {circumflex over (p)} _(m)(t _(G)), σ_(m) ^(z)(t _(G)))

where ŷ_(ROI,m) ^((i+1)) is a m^(th) element of the receiving signal obtained in S43;

S56, for n_(s)=1,2, calculating observed mean value {circumflex over (v)}_(n) _(s) (t_(G)) and variance σ_(n) _(s) ^(v)(t_(G)) of {circumflex over (x)}_(n) _(s) (t_(G)) as follows:

{circumflex over (v)} _(n) _(s) (t _(G))=(t _(G))+σ_(n) _(s) (t _(G))Σ_(m) A _(m,n) _(s) ŝ _(m)(t _(G))

σ_(n) _(s) ^(v)(t _(G))=[Σ_(n) _(s) A _(m,n) _(s) ²σ_(n) _(s) ^(s)(t _(G))]⁻¹;

S57, for n_(s)=1,2, . . . , N_(s), calculating observed mean value {circumflex over (x)}_(n) _(s) (t_(G)+1) and variance σ_(n) _(s) ^(x)(t_(G)+1) as follows:

{circumflex over (x)} _(n) _(s) (t _(G)+1)=g _(in)(t _(G) , {circumflex over (v)} _(n) _(s) (t _(G)), σ_(n) _(s) ^(v)(t _(G)),q)

σ_(n) _(s) ^(x)(t _(G)+1)=σ_(n) _(s) ^(v)(t _(G))g′ _(in)(t _(G) ,{circumflex over (v)} _(n) _(s) (t _(G)), σ_(n) _(s) ^(r)(t _(G)),q)

S58, repeating steps S54 to S57 until the convergence condition Σ_(m)|y_(m)−{circumflex over (z)}_(m)(t_(G))|>ε_(G) is satisfied;

S59, taking the sparse variable {circumflex over (x)}_(n) _(s) (t_(G)) estimated in the above steps as a final environment sensing result of the current iteration.

The present disclosure has the following beneficial effects: in the uplink wireless communication scene, the present disclosure provides a design method for integrated millimeter wave sensing and communication system by using the existing communication equipment, and fully utilizes different system resources to realize focused environmental sensing based on data sent by users; the iterative focused environmental sensing method provided by the present disclosure solves the problem of low accuracy of large-scale environmental sensing due to insufficient system resources; the present disclosure overcomes the defect that the traditional compressed sensing algorithm cannot focus on a specific range of environmental variables, while in the iterative process of the algorithm, the prior probability of environmental variables is estimated step by step according to the reconstruction result of compressed sensing in each step, thus realizing an iterative progressive compressed sensing sparse reconstruction for a specific target. On the basis of the same system resource overhead, the algorithm of the present disclosure significantly improves the sensing accuracy of a specific target and is superior to the existing algorithms.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a schematic diagram of a two-dimensional focused millimeter wave environment sensing scenario provided by an exemplary embodiment;

FIG. 2 is a flowchart of an iterative algorithm provided by an exemplary embodiment;

FIG. 3 is a diagram showing the relationship between the number of users and the environmental sensing accuracy MSE when comparing the present disclosure with other compressed sensing reconstruction algorithms provided by an exemplary embodiment;

FIG. 4 is a diagram showing the relationship between the number of subcarriers and the environmental sensing accuracy MSE when comparing the present disclosure with other compressed sensing reconstruction algorithms provided by an exemplary embodiment.

DESCRIPTION OF EMBODIMENTS

In order to better understand the technical solution of the present disclosure, the embodiments of the present disclosure will be described in detail with reference to the attached drawings.

It should be clear that the described embodiments are only part of, not all of the embodiment of this present disclosure. Based on the embodiments in this present disclosure, all other embodiments obtained by those skilled in the art without creative work belong to the protection scope of this present disclosure.

A single-cell uplink communication system is taken into consideration, in which a multi-antenna BS serves multiple single-antenna users. In order to sense a specific target, all users send uplink communication signals to the base station at the same time. Due to a large amount of scattering in the environment, the transmitted signal of each user propagates through multiple paths. Therefore, the signal received by the base station contains abundant environmental scattering information in order that the base station can process the receiving signal to realize environmental sensing. As shown in FIG. 1 , considering a simplified two-dimensional scene model, the analysis method of three-dimensional scenario can also be deduced. Gray target scatters are scatters to be imaged accurately, and the rest are background scatters that will not be considered.

The present disclosure provides an iterative focused millimeter wave integrated communication and sensing method, which includes the following steps:

S1, in any time slot, a base station receives pilot frequency sequence signals with a certain length sent by all active users in an environment to obtain receiving signals; the receiving signals are signals after the pilot frequency sequence signals are influenced by the environment.

S2, an environmental sensing problem of a specific target is converted into a compressed sensing reconstruction problem by using the receiving signals in the step S1 based on a multi-beam multi-carrier millimeter wave channel model.

In an embodiment, step S2 specifically includes the following steps:

S21, environmental information in the receiving signals in step S1 is discretized into pixels; each pixel represents environmental information in a small square with a surrounding size of l_(s)×w_(s), and if an environmental size of a whole range is L_(s)×W_(s), a total number of the pixels is N_(s)=L/l_(s)×W/w_(s); an interior of each pixel may be empty, or there may be scatters; a scattering coefficient x_(n) _(s) is used to represent the scattering coefficient of a small cube where a n_(s) ^(th) point cloud is located; if an interior of the small cube is empty, then x_(n) _(s) =0; therefore, the environmental information of a whole room can be expressed as x=[x₁,x₂, . . . , x_(N) _(s) ]^(T).

S22, a multi-beam multi-carrier millimeter wave channel model is used, and at an n_(f) ^(th) subcarrier frequency, the receiving signals received by a receiving antenna of the base station are expressed as follows:

y _(n) _(f) =w _(n) _(f) (H _(n) _(f) ^(s→B)diag(δx)H _(n) _(f) ^(u→s) +H _(n) _(f) ^(LOS))s _(n) _(f) +n=w _(n) _(f) (H _(n) _(f) ^(NLOS) +H _(n) _(f) ^(LOS))s _(n) _(f) +n

where y_(n) _(f) ∈

^(N) ^(c) ^(xK) represents the receiving signals with a length of K code elements of RF links of N_(c) base stations w_(n) _(f) ∈

^(N) ^(c) ^(xN) ^(R) is a beam forming vector of N_(R) uniform linear array receiving antennas of the base stations, δ is a normalized coefficient of a scattering coefficient, which is selected according to a pixel size l_(s)×w_(s) and describes the physical relationship between an electromagnetic wave receiving region and a receiving power s_(n) _(f) ∈

^(N) ^(u) ^(xK) represents pilot frequencies with a length of K code elements sent by N_(u) users, n is noise; H_(n) _(f) ^(LOS) represents a free-space propagation channel from N_(u) users to N_(R) receiving antennas at an n_(f) ^(th) subcarrier frequency; and H_(n) _(f) ^(NLOS) is a NLOS channel on a nfth subcarrier.

H _(n) _(f) ^(LOS) is expressed as

H _(n) _(f) ^(LOS) =e _(n) _(f) ^(LOS) G _(n) _(f) ^(LOS)

where e_(n) _(f) ^(LOS) is a steering vector of N_(u) users and G_(n) _(f) ^(LOS) is a channel gain from N_(u) users to the base station;

${e_{n_{f}}^{LOS}\left( {n_{R},n_{u}} \right)} = {e^{j\frac{2\pi}{\lambda_{n_{f}}}{({n_{R} - 1})}{dsin}\theta_{n_{u}}^{LOS}}/\sqrt{N_{R}}}$

where j represents a complex code element, n_(R) is a serial number of the receiving antenna, θ_(n) _(u) ^(LOS) is an arrival angle of a n_(u) ^(th) user, and d is a uniform linear array antenna spacing deployed by the base station, λ_(n) _(f) is a wavelength; G_(n) _(f) ^(LOS) is expressed as follows:

G_(n_(f))^(LOS) = diag([g_(n_(f), 1)^(LOS)e^(jφ_(n_(f), 1)^(LOS)), …, g_(n_(f), N_(u))^(LOS)e^(jφ_(n_(f), N_(u))^(LOS))])

where g_(n) _(f,) _(n) _(u) ^(LOS) and φ_(n) _(f,) _(n) _(u) ^(LOS) are a channel amplitude gain and a phase shift from the n_(u) ^(th) user to the base station, respectively.

At the n_(f) ^(th) subcarrier frequency, a free-space propagation channel H_(n) _(f) ^(u→s)(n_(s), n_(u)) from the n_(u) ^(th) user to a n_(s) ^(th) pixel is expressed as:

H_(n_(f))^(u → s)(n_(s), n_(u)) = g_(n_(f))^(u → s)(n_(s), n_(u))e^(jφ_(n_(f))^(u → s)(n_(s), n_(u)))

where g_(n) _(f) ^(u→s)(n_(s), n_(u)) and φ_(n) _(f) ^(u→s)(n_(s), n_(u)) are a channel amplitude gain and a phase shift from n_(u) ^(th) user to the n_(s) ^(th) pixel, respectively.

At the n_(f) ^(th) subcarrier frequency, a free-space propagation channel H_(n) _(f) ^(s→B)∈

^(N) ^(R) ^(xN) ^(s) from N_(s) pixels to N_(R) receiving antennas is expressed as:

H _(n) _(f) ^(s→B) =e _(n) _(f) ^(s→B) G _(n) _(f) ^(s→B)

where e_(n) _(f) ^(s→B) is a steering vector of N_(s) pixels and G_(n) _(f) ^(s→B) is a channel gain from N_(s) pixels to the base station.

${e_{n_{f}}^{s\rightarrow B}\left( {n_{R},n_{s}} \right)} = {e^{j\frac{2\pi}{\lambda_{n_{f}}}{({n_{R} - 1})}{dsin}\theta_{n_{s}}^{s\rightarrow B}}/\sqrt{N_{R}}}$

where n_(R) is a receiving antenna number, θ_(n) _(s) ^(s→B) an arrival angle of the n_(s) ^(th) pixel, and G_(n) _(f) ^(s→B) is expressed as follows:

G_(n_(f))^(s → B) = diag([g_(n_(f), 1)^(s → B)e^(jφ_(n_(f), 1)^(s → B)), …, g_(n_(f), N_(s))^(s → B)e^(jφ_(n_(f), N_(s))^(s → B))])

where g_(n) _(f) _(n) _(s) ^(s→B) and φ_(n) _(f) _(n) _(s) ^(s→B) are a channel amplitude gain and a phase shift from the n_(s) ^(th) pixel to the base station, respectively.

S23, an estimation result of the environmental information is expressed as {circumflex over (x)}, which is expressed as follows:

{circumflex over (x)}=argmin_(x) _(ROI) ||x|| ₀ s.t. ||y−w(H ^(NLOS) +H ^(LOS))s|| ₂≤ε

where y is a receiving signal of all subcarriers, w is a beam forming vector of the uniform linear array receiving antenna of all subcarriers, x_(ROI) is environmental information in a region of interest, H^(NLOS) is a NLOS channel of all subcarriers, H^(LOS) is a LOS channel of all subcarriers, s is a transmitted signal of the NLOS channel of all subcarriers, and ε is a relaxation variable.

Since a free-space channel coefficient of a direct-view channel can be estimated by a numerical model, at the n_(f) ^(th) subcarrier frequency, part of the receiving signal ŷ_(n) _(f) containing unknown environmental information is expressed as,

{tilde over (y)} _(n) _(f) =w _(n) _(f) H _(n) _(f) ^(s→B)diag(δx)H _(n) _(f) ^(u→s) s _(n) _(f) +n

by combining data of N_(f) subcarriers, an iterative focused environmental sensing problem of a specific target is converted into a compressed sensing reconstruction problem equation as follows:

$\begin{bmatrix} {{\overset{\sim}{y}}_{1}\left( {:,1} \right)} \\  \vdots \\ {{\overset{\sim}{y}}_{1}\left( {:,K} \right)} \\  \vdots \\ {{\overset{\sim}{y}}_{N_{f}}\left( {:,1} \right)} \\  \vdots \\ {{\overset{\sim}{y}}_{N_{f}}\left( {:,K} \right)} \end{bmatrix}_{N_{c}N_{f}K \times 1} = {\left. {{{\delta\begin{bmatrix} {w_{1}H_{1}^{s\rightarrow B}{{diag}\left( {H_{1}^{u\rightarrow s}{s_{1}\left( {:,1} \right)}} \right)}} \\  \vdots \\ {w_{1}H_{1}^{s\rightarrow B}{{diag}\left( {H_{1}^{u\rightarrow s}{s_{1}\left( {:,K} \right)}} \right)}} \\  \vdots \\ {w_{N_{f}}H_{N_{f}}^{s\rightarrow B}{{diag}\left( {H_{N_{f}}^{u\rightarrow s}{s_{N_{f}}\left( {:,1} \right)}} \right)}} \\  \vdots \\ {w_{N_{f}}H_{N_{f}}^{s\rightarrow B}{{diag}\left( {H_{N_{f}}^{u\rightarrow s}{s_{N_{f}}\left( {:,K} \right)}} \right)}} \end{bmatrix}}_{N_{c}N_{f}K \times N_{s}}\lbrack x\rbrack}_{N_{s} \times 1} + n}\Rightarrow\overset{\sim}{y} \right. = {{Ax} + {n.}}}$

S3, the compressed sensing reconstruction problem in step S2 is solved based on an approximate message passing method to obtain a coarse initial result of environment sensing;

in an embodiment, step S3 specifically includes the following steps:

S31, firstly, an initial coarse environmental sensing prior probability is set, and the environmental information is set to be a Bernoulli-Gaussian distribution, wherein a probability density function p_(x)(x|q) is expressed as:

p _(x)(x|q)=(1−λ)δ(x)+λN(x|θ ^(x), σ^(x))

where x represents an element in the environmental information x, all parameters are expressed as q

[λ, θ^(x),σ^(x)], δ(·) is an impulse function, λ is a sparse coefficient; θ^(x)∈[0,1] and σ^(x) are a mean value and a variance of environmental information distribution, respectively, and N(·) represents a standard normal distribution;

S32, approximate message passing algorithm parameters are initialized, and the input functions g_(in)(·), g′_(in)(·) and output functions g_(out)(·), g′_(out)(·) are as follows:

${{g_{in}\left( {\hat{v},\sigma^{v},q} \right)} = {\arg\max\limits_{x}{F_{in}\left( {x,\hat{v},\sigma^{v},q} \right)}}}{{F_{in}\left( {x,\hat{v},\sigma^{v},q} \right)} = {{\log{p_{x}\left( {x❘q} \right)}} - {\frac{1}{2\sigma^{v}}\left( {\hat{v} - x} \right)^{2}}}}{{g_{in}^{\prime}\left( {\hat{v},\sigma^{v},q} \right)} = \frac{1}{1 - {\sigma^{v}{\frac{\partial^{2}}{\partial x^{2}}{\log\left\lbrack {p_{x}\left( {x❘q} \right)} \right\rbrack}}}}}{{g_{out}\left( {y,\hat{p},\sigma^{z}} \right)} = \frac{y - \hat{p}}{\sigma^{w} + \sigma^{z}}}{{g_{out}^{\prime}\left( {y,\hat{p},\sigma^{z}} \right)} = {- \frac{1}{\sigma^{w} + \sigma^{z}}}}$

where {circumflex over (v)}, σ^(v), {circumflex over (p)}, σ^(z) are input variables and σ^(w) is a noise variance.

Let a number of iterations t_(G)=0, a residual ŝ(−1)=0, a sparse vector estimated mean value {circumflex over (x)}_(n) _(s) (t_(G))>0, and a sparse vector estimated variance σ_(n) _(s) ^(x)(t_(G))>0.

S33, let M=N_(c)N_(f)K, where N_(c) is a number of base stations, a is a number of code elements, N_(f) is a number of subcarriers; for m=1,2, . . . , M, estimated mean value {circumflex over (z)}_(m)(t_(G)) and variance σ_(m) ^(z)(t_(G)) of a variable z_(m) are calculated:

σ_(m) ^(z)(t _(G))=Σ_(n) _(s) A _(m,n) _(s) ²σ_(n) _(s) ^(x)(t _(G))

{circumflex over (p)} _(m)(t _(G))=Σ_(n) _(s) A _(m,n) _(s) {circumflex over (x)} _(n) _(s) (t _(G))−σ_(m) ^(z)(t)ŝ _(m)(t _(G)−1)

{circumflex over (z)} _(m)(t _(G))=Σ_(n) _(s) A _(m,n) _(s) {circumflex over (x)} _(n) _(s) (t _(G))

S34, for m=1,2, . . . , M, a mean value ŝ_(m)(t_(G)) and a variance σ_(m) ^(s)(t_(G)) of the residual are calculated:

ŝ _(m)(t _(G))=g _(out)(t _(G) , y _(m) , {circumflex over (p)} _(m)(t _(G)), σ_(m) ^(z)(t _(G)))

σ_(m) ^(s)(t _(G))=−g′ _(out)(t _(G) , y _(m) , {circumflex over (p)} _(m)(t _(G)), σ_(m) ^(z)(t _(G)))

where y_(m) is the m^(th) element of the receiving signal;

S35, for n_(s)=1,2, . . . , N_(s), observed mean value {circumflex over (v)}_(n) _(s) (t_(G)) and variance σ_(n) _(s) ^(v)(t_(G)) of {circumflex over (x)}_(n) _(s) (t_(G)) are calculated:

{circumflex over (v)} _(n) _(s) (t _(G))={circumflex over (x)} _(n) _(s) (t _(G))+σ_(n) _(s) ^(v)(t _(G))Σ_(m) A _(m,n) _(s) ŝ _(m)(t _(G))

σ_(n) _(s) ^(v)(t _(G))=[Σ_(n) _(s) A _(m,n,n) _(s) σ_(n) _(s) ^(s)(t _(G))]⁻¹

S36, for n_(s)=1,2, . . . , N_(s), observed mean value {circumflex over (x)}_(n) _(s) (t_(G)+1) and variance σ_(n) _(s) ^(x)(t_(G)+1) of x_(n) _(s) are calculated:

{circumflex over (x)} _(n) _(s) (t _(G)+1)=g _(in)(t _(G) , {circumflex over (v)} _(n) _(s) (t _(G)), σ_(n) _(s) ^(v)(t _(G)), q)

σ_(n) _(s) ^(x)(t _(G)+1)=σ_(n) _(s) ^(v)(t _(G))g′ _(in)(t _(G) , {circumflex over (v)} _(n) _(s) (t _(G)), σ_(n) _(s) ^(r)(t _(G)), q)

S37, step S33 to step S36 are repeatedly executed until a convergence condition Σ_(m)|y_(m)−{circumflex over (z)}_(m)(t_(G))|>ε_(G) is satisfied, where ε_(G) is an error tolerance;

S38, a sparse variable {circumflex over (x)}_(n) _(s) (t_(G)) is taken as a coarse environmental sensing initial result of the environmental information x.

S4, a predetermined region is selected as a focused region of interest from the whole environment based on the coarse initial result of environmental sensing, and the target object in the region of interest is divided and determined according to a background determining method and the influence of background scatters outside the region of interest on the receiving signals is removed to obtain receiving signals corresponding to the target object;

In an embodiment, step S4 is specifically:

S41, a predetermined region as a focused region of interest from the whole environment according to the coarse environmental sensing initial result and actual needs; the target object is in the region of interest;

S42, in an ith iteration, a background scatterer {circumflex over (x)}_(back) ^((i))(n_(s)) outside the region of interest is detected as follows:

${{\hat{x}}_{back}^{(i)}\left( n_{s} \right)} = \left\{ \begin{matrix} {0,} & {{{\hat{x}}^{(i)}\left( n_{s} \right)} \leq {\gamma_{i}{or}{{\hat{x}}^{(i)}\left( n_{s} \right)}{inside}{{ROI}.}}} \\ {{{\hat{x}}^{(i)}\left( n_{s} \right)},} & {{{\hat{x}}^{(i)}\left( n_{s} \right)} \geq \gamma_{i}} \end{matrix} \right.$

where {circumflex over (x)}^((i))(n_(s)) represents a result in the ith iteration, y_(i) is a detection threshold of the background scatterer, and the detection threshold y_(i) shall decrease with the increase of the number of iterations;

S43, a background scattering part from the receiving signal is removed to obtain a receiving signal ŷ_(ROI) ^((i+1)) of the target object in ROI of an i+1^(st) iteration:

Ŷ _(ROI) ^((i+1))=(1−a){tilde over (y)}+a(ŷ _(ROI) ^((i)) −Ax _(back) ^((i)))

where a is a weight variable, which is used to enhance the robustness of iterative algorithm, and the weight variable a should increase with the increase of the number of iterations.

S5, an environmental sensing result is calculated based on the receiving signals corresponding to the target object obtained in the step S4;

In an embodiment, step S5 specifically includes the following steps:

S51, the prior probability of the environmental information in an iterative focused process is set; in the i^(th) iteration, it is assumed that the background scatterer obeys Bernoulli Gaussian distribution, and a prior probability formula p(x_(back)) is as follows:

p(x _(back))=(1−λ)δ(x _(back))+λ

(x _(back); θ_(back,i), σ_(back))

where θ_(back,i) and σ_(back) represent the mean value and the variance of the background environmental information distribution, respectively, λ is a sparse coefficient, N(·) represents a standard normal distribution and x_(back) represents the background scatterer.

The scatterer distribution in the selected ROI is a Gaussian distribution, and there is no sparsity.

p(x _(ROI))=

(x _(ROI); θ_(ROI), σ_(ROI))

where θ_(ROI) and σ_(ROI) represent the mean value and variance of ROI environmental information distribution, respectively;

S52, according to the prior probability formula obtained in step S51, the prior probability p(x) of environmental information inside and outside the region of interest in the current i+1^(st) iteration is set, x={x_(ROI), x_(back)}.

S53, the approximate message passing algorithm parameters are initialized, and let the input functions g_(in)(·), g′_(in)(·) and the output functions g_(out)(·), g′_(in)(·) be as follows:

${{g_{in}\left( {\hat{v},\sigma^{v},q} \right)} = {\arg\max\limits_{x}{F_{in}\left( {x,\hat{v},\sigma^{v},q} \right)}}}{{F_{in}\left( {x,\hat{v},\sigma^{v},q} \right)} = {{\log{p_{x}\left( {x❘q} \right)}} - {\frac{1}{2\sigma^{v}}\left( {\hat{v} - x} \right)^{2}}}}{{g_{in}^{\prime}\left( {\hat{v},\sigma^{v},q} \right)} = \frac{1}{1 - {\sigma^{v}\frac{\partial^{2}}{\partial x^{2}}{\log\left\lbrack {p_{x}\left( {x❘q} \right)} \right\rbrack}}}}{{g_{out}\left( {y,\hat{p},\sigma^{z}} \right)} = \frac{y - \hat{p}}{\sigma^{w} + \sigma^{z}}}{{g_{out}^{\prime}\left( {y,\hat{p},\sigma^{z}} \right)} = {- \frac{1}{\sigma^{w} + \sigma^{z}}}}$

Let the number of iterations t_(G)=0, the residual Ŝ(−1)=0, the sparse vector estimated mean value {circumflex over (x)}_(n) _(s) (t_(G))>0 and the sparse vector estimate variance σ_(n) _(s) ^(x)(t_(G))>0;

S54, let M=N_(c)n_(f)K, and for m=1,2, . . . , M, estimated mean value {circumflex over (z)}_(m)(t_(G)) and variance σ_(m) ^(z)(t_(G)) of z_(m) are calculated, which is specifically as follows:

σ_(m) ^(z)(t _(G))=Σ_(n) _(s) A _(m,n) _(s) ^(x)(t _(G))

{circumflex over (p)} _(m)(t _(G))=Σ_(n) _(s) A _(m,n) _(s) {circumflex over (x)} _(n) _(s) (t _(G))−σ_(m) ^(z)(t)ŝ _(m)(t_(G)−1)

{circumflex over (z)} _(m)(t _(G))=Σ_(n) _(s) A _(m,n) _(s) {circumflex over (x)} _(n) _(s) (t _(G))

S55, for m=1,2, . . . , M, calculating a mean value ŝ_(m)(t_(G)) and a variance σ_(m) ^(s)(t_(G)) of the residual, which is specifically as follows:

ŝ _(m)(t _(G))=g _(out)(t _(G) , ŷ _(ROI,m) ^((i+1)) , {circumflex over (p)} _(m)(t _(G)), σ_(m) ^(z)(t _(G)))

σ_(m) ^(s)(t _(G))=−g′ _(out)(t _(G) , ŷ _(ROI,m) ^((i+1)) , {circumflex over (p)} _(m)(t _(G)), σ_(m) ^(z)(t _(G)))

where ŷ_(ROI,m) ^((i+1)) is a m^(th) element of the receiving signal obtained in S43;

S56, for n_(s)=1,2, N_(s), observed mean value {circumflex over (v)}_(n) _(s) (t_(G)) and variance σ_(n) _(s) ^(v)(t_(G)) of {circumflex over (x)}_(n) _(s) (t_(G)) as follows:

{circumflex over (v)} _(n) _(s) (t _(G))={circumflex over (x)} _(n) _(s) (t _(G))+σ_(n) _(s) (t _(G))Σ_(m) A _(m,n) _(s) ŝ _(m)(t _(G))

σ_(n) _(s) ^(v)(t _(G))=[Σ_(n) _(s) A _(m,n) _(s) ²σ_(n) _(s) ^(s)(t _(G))]⁻¹;

S57, for n_(s)=1,2, . . . , N_(s), observed mean value {circumflex over (x)}_(n) _(s) (t_(G)+1) and variance σ_(n) _(s) ^(x)(t_(G)+1) as follows:

{circumflex over (x)} _(n) _(s) (t _(G)+1)=g _(in)(t _(G) , {circumflex over (v)} _(n) _(s) (t _(G)), σ_(n) _(s) ^(v)(t _(G)),q)

σ_(n) _(s) ^(x)(t _(G)+1)=σ_(n) _(s) ^(v)(t _(G))g′ _(in)(t _(G) ,{circumflex over (v)} _(n) _(s) (t _(G)), σ_(n) _(s) ^(r)(t _(G)),q)

S58, steps S54 to S57 are repeated until the convergence condition Σ_(m)|y_(m)−{circumflex over (z)}_(m)(t_(G))|>ε_(G) is satisfied;

S59, the sparse variable {circumflex over (x)}_(n) _(s) (t_(G)) estimated in the above steps is taken as a final environment sensing result of the current iteration.

S6, step S4 and step S5 are repeated in sequence until the algorithm convergence, the iterative flow chart is shown in FIG. 2 , and the final environment sensing result is obtained.

As can be seen from computer simulation: as shown in FIGS. 3 and 4 , the imaging effect between the focused method of the present disclosure and the large-scale imaging algorithm is compared. Compared with large-scale imaging, the algorithm of the present disclosure significantly improves the imaging accuracy of objects in ROI. FIG. 3 shows that with the increase of the number of users, the environmental sensing effect of the method of the present disclosure is gradually improved and superior to the existing algorithms. FIG. 4 shows that with the increase of the number of subcarriers, the environmental sensing effect of the method of the present disclosure is gradually improved and superior to the existing algorithms.

In the uplink wireless communication scenario, the design method for integrated millimeter wave sensing and communication system by using the existing communication equipment fully utilizes different system resources to realize focused environmental sensing based on the data sent by users, converts the environmental sensing problem into a compressed sensing reconstruction problem, and then realizes the initial coarse sensing of the environment based on an approximate message passing algorithm. According to a background determining method, in the present disclosure, the target object is divided and determined, and the influence of the background scatterer on the receiving signal is removed, and finally, the background scatterer is repeatedly removed, so as to obtain a more accurate focused sensing result of the target object. Compared with the existing environmental sensing reconstruction algorithms, the iterative focused environmental sensing method provided by the present disclosure solves the problem of low precision of large-scale environmental sensing due to insufficient system resources, improves the defect that the traditional compressed sensing algorithm cannot focus on a specific range of environmental variables, thereby providing an efficient environment sensing method for the future design of integrated sensing and communication system. In the iterative process of the algorithm, according to the results of each step of compressed sensing reconstruction, the prior probability of environmental variables is estimated step by step, and an iterative progressive compressed sensing sparse reconstruction is realized for a specific target. On the basis of the same system resource overhead, the algorithm of the present disclosure significantly improves the sensing accuracy of a specific target and is superior to the existing algorithms.

The above is only preferred embodiments of one or more embodiments of this specification, and is not intended to limit one or more embodiments of this specification. Any modification, equivalent substitution, improvement and the like made within the spirit and principle of one or more embodiments of this description shall be included in the scope of protection of one or more embodiments of this description. 

What is claimed is:
 1. An iterative focused millimeter wave integrated communication and sensing method, which is applied to uplink wireless communication, comprising the following steps: S1, in any time slot, receiving, by a base station, pilot frequency sequence signals with a certain length sent by all active users in an environment to obtain receiving signals, wherein the receiving signals are signals after the pilot frequency sequence signals are influenced by environment; S2, converting an environmental sensing problem of a specific target into a compressed sensing reconstruction problem using the receiving signals in the step S1 based on a multi-beam multi-carrier millimeter wave channel model; S3, solving the compressed sensing reconstruction problem in the step S2 based on an approximate message passing method to obtain a coarse initial result of environment sensing; S4, selecting a predetermined region as a focused region of interest from whole environment based on the coarse initial result of environmental sensing, and dividing and determining a target object in the region of interest according to a background determining method and removing influence of background scatters outside the region of interest on the receiving signals to obtain receiving signals corresponding to the target object; S5, calculating an environmental sensing result based on the receiving signals corresponding to the target object obtained in the step S4; and S6, repeating the steps S4 and S5 in sequence until the algorithm convergence, to obtain a final environment sensing result.
 2. The method according to claim 1, wherein the step S2 comprises the following sub-steps: S21, discretizing environmental information in the receiving signals in the step S1 into pixels, wherein each of the pixels represents environmental information in a small square with a surrounding size of l_(s)×w_(s), letting an environmental size of a whole range is L_(s)×W_(s), a total number of the pixels being N_(s)−L/l_(s)×W/w_(s); each of the pixels is empty, or has scatters inside, wherein a scattering coefficient x_(n) _(s) is used to represent a scattering coefficient of a small cube where a n_(s) ^(th) point cloud is located, when an interior of the small cube is empty, x_(n) _(s) =0, and environmental information of a whole room is expressed as x=[x₁, x₂, . . . , x_(n) _(s) ]^(T); S22, constructing a multi-beam multi-carrier millimeter wave channel model, wherein at an n_(f) ^(th) subcarrier frequency, the receiving signals received by a receiving antenna of the base station are expressed as follows: y _(n) _(f) =w _(n) _(f) (H _(n) _(f) ^(s→B)diag(δx)H _(n) _(f) ^(u→s) +H _(n) _(f) ^(LOS))s _(n) _(f) +n=w _(n) _(f) (H _(n) _(f) ^(NLOS) +H _(n) _(f) ^(LOS))s _(n) _(f) +n where y_(n) _(f) ∈

^(N) ^(c) ^(xK) represents the receiving signals with a length of K code elements of RF links of N_(c) base stations, w_(n) _(f) ε

^(N) ^(c) ^(xN) ^(R) represents a beam forming vector of N_(R) uniform linear array receiving antennas of the base stations, δ represents a normalized coefficient of a scattering coefficient, selected according to a pixel size i_(s)×w_(s), wherein a normalized coefficient defines a physical relationship between an electromagnetic wave receiving region and a receiving power, s_(n) _(f) ε

^(N) ^(u) ^(xK) represents pilot frequencies with a length of K code elements sent by N_(u) users, n represents noise; H_(n) _(f) ^(LOS) represents a free-space propagation channel from N_(u) users to N_(R) receiving antennas at an n_(f) ^(th) subcarrier frequency; and H_(n) _(f) ^(LOS) represents a Non-Line-of-Sight (NLOS) channel on an n_(f) ^(th) subcarrier; wherein H_(n) _(f) ^(LOS) is expressed as follows: H _(n) _(f) ^(LOS) =e _(n) _(f) ^(LOS) G _(n) _(f) ^(LOS) where e_(n) _(f) ^(LOS) represents a steering vector of N_(u) users and G_(n) _(f) ^(LOS) represents a channel gain from N_(u) users to the base station; wherein e_(n) _(f) ^(LOS) is expressed as follows: ${e_{n_{f}}^{LOS}\left( {n_{R},n_{u}} \right)} = {e^{j\frac{2\pi}{\lambda_{n_{f}}}{({n_{R} - 1})}{dsin}\theta_{n_{u}}^{LOS}}/\sqrt{N_{R}}}$ where j represents a complex code element, n_(R) represents a serial number of the receiving antenna, θ_(n) _(u) ^(LOS) represents an arrival angle of an n_(u) ^(th) user, and d represents a uniform linear array antenna spacing deployed by the base station, and λ_(n) _(f) represents a wavelength; wherein G_(n) _(f) ^(LOS) is expressed as follows: G_(n_(f))^(LOS) = diag([g_(n_(f), 1)^(LOS)e^(jφ_(n_(f), 1)^(LOS)), …, g_(n_(f), N_(u))^(LOS)e^(jφ_(n_(f), N_(u))^(LOS))]) where g_(n) _(f,) _(n) _(u) ^(LOS) and φ_(n) _(f,) _(n) _(u) ^(LOS) represent a channel amplitude gain and a phase shift from the n_(u) ^(th) user to the base station, respectively; wherein at the n_(f) ^(th) subcarrier frequency, a free-space propagation channel H_(n) _(f) ^(u→s)(n_(s), n_(u)) from the n_(u) ^(th) user to an n_(s) ^(th) pixel is expressed as: H_(n_(f))^(u → s)(n_(s), n_(u)) = g_(n_(f))^(u → s)(n_(s), n_(u))e^(jφ_(n_(f))^(u → s)(n_(s), n_(u))) where g_(n) _(f) ^(u→s)(n_(s), n_(u)) and φ_(n) _(f) ^(u→s)(n_(s), n_(u)) are a channel amplitude gain and a phase shift from n_(u) ^(th) user to the n_(s) ^(th) pixel, respectively; wherein at the n_(f) ^(th) subcarrier frequency, a free-space propagation channel H_(n) _(f) ^(s→B)∈

^(N) ^(R) ^(xN) ^(s) from N_(s) pixels to N_(R) receiving antennas is expressed as: H _(n) _(f) ^(s→B) =e _(n) _(f) ^(s→B) G _(n) _(f) ^(s→B) where e_(n) _(f) ^(s→B) represents a steering vector of N_(s) pixels and e_(n) _(f) ^(s→B) represents a channel gain from N_(s) pixels to the base station; ${e_{n_{f}}^{s\rightarrow B}\left( {n_{R},n_{s}} \right)} = {e^{j\frac{2\pi}{\lambda_{n_{f}}}{({n_{R} - 1})}{dsin}\theta_{n_{s}}^{s\rightarrow B}}/\sqrt{N_{R}}}$ where n_(R) represents a receiving antenna number, θ_(n) _(s) ^(s→B) represents an arrival angle of the n_(s) ^(th) pixel, and wherein G_(n) _(f) ^(s→B) is expressed as follows: G_(n_(f))^(s → B) = diag([g_(n_(f), 1)^(s → B)e^(jφ_(n_(f^(, 1)))^(s → B)), …, g_(n_(f), N_(s))^(s → B)e^(jφ_(n_(f), N_(s))^(s → B))]) where g_(n) _(f,) _(n) _(s) ^(s→B) and φ_(n) _(f,) _(n) _(s) ^(s→B) and represent a channel amplitude gain and a phase shift from the n_(s) ^(th) pixel to the base station, respectively; and S23, expressing an estimation result of environmental information as {circumflex over (x)}, wherein {circumflex over (x)} is expressed as follows: {circumflex over (x)}=argmin_(x) _(ROI) ||x|| ₀ s.t. ||y−w(H ^(NLOS) +H ^(LOS))s|| ₂≤ε where y is a receiving signal of all subcarriers, w represents a beam forming vector of the uniform linear array receiving antenna of all subcarriers, x_(ROI) represents environmental information in a region of interest, H^(NLOS) represents a NLOS channel of all subcarriers, H^(LOS) represents a LOS channel of all subcarriers, s represents a transmitted signal of the NLOS channel of all subcarriers, and ε represents a relaxation variable; expressing, at the n_(f) ^(th) subcarrier frequency, part of the receiving signal {tilde over (y)}_(n) _(f) containing unknown environmental information as follows: {tilde over (y)} _(n) _(f) =w _(n) _(f) H _(n) _(f) ^(s→B)diag(δx)H _(n) _(f) ^(u→s) S _(n) _(f) +n wherein a free-space channel coefficient of a direct-view channel is estimated by a numerical model, and converting, by combining data of N_(f) subcarriers, an iterative focused environmental sensing problem of a specific target into a compressed sensing reconstruction problem equation as follows: $\begin{bmatrix} {{\overset{\sim}{y}}_{1}\left( {:,1} \right)} \\  \vdots \\ {{\overset{\sim}{y}}_{1}\left( {:,K} \right)} \\  \vdots \\ {{\overset{\sim}{y}}_{N_{f}}\left( {:,1} \right)} \\  \vdots \\ {{\overset{\sim}{y}}_{N_{f}}\left( {:,K} \right)} \end{bmatrix}_{N_{c}N_{f}K \times 1} = {\left. {{{\delta\begin{bmatrix} {w_{1}H_{1}^{s\rightarrow B}{{diag}\left( {H_{1}^{u\rightarrow S}{s_{1}\left( {:,1} \right)}} \right)}} \\  \vdots \\ {w_{1}H_{1}^{s\rightarrow B}{{diag}\left( {H_{1}^{u\rightarrow s}{s_{1}\left( {:,K} \right)}} \right)}} \\  \vdots \\ {w_{N_{f}}H_{N_{f}}^{s\rightarrow B}{{diag}\left( {H_{N_{f}}^{u\rightarrow s}{s_{N_{f}}\left( {:,1} \right)}} \right)}} \\  \vdots \\ {w_{N_{f}}H_{N_{f}}^{s\rightarrow B}{{diag}\left( {H_{N_{f}}^{u\rightarrow s}{s_{N_{f}}\left( {:,K} \right)}} \right)}} \end{bmatrix}}_{N_{c}N_{f}K \times N_{s}}\lbrack x\rbrack}_{N_{s} \times 1} + n}\Rightarrow\overset{\sim}{y} \right. = {{Ax} + {n.}}}$
 3. The method according to claim 2, wherein the step S3 comprises the following steps: S31, firstly setting an initial coarse environmental sensing prior probability, and letting the environmental information be a Bernoulli-Gaussian distribution, wherein a probability density function p_(x)(x|q) is expressed as: p _(x)(x|q)=(1−λ)δ(x)+λN(x|θ ^(x),σ^(x)) where x represents an element in environmental information x, all parameters are expressed as q

[λ,θ^(x), σ^(x)], δ(·) represents an impulse function, λ represents a sparse coefficient; θ^(x)∈[0,1] and σ^(x) represent a mean value and a variance of environmental information distribution, respectively, and N(·) represents a standard normal distribution; S32, initializing approximate message passing algorithm parameters, and letting input functions g_(in)(·), g′_(in)(·) and output functions g_(out)(·), g′_(out)(·) be as follows, respectively ${{g_{in}\left( {\hat{v},\sigma^{v},q} \right)} = {\arg\max\limits_{x}{F_{in}\left( {x,\hat{v},\sigma^{v},q} \right)}}}{{F_{in}\left( {x,\hat{v},\sigma^{v},q} \right)} = {{\log{p_{x}\left( {x❘q} \right)}} - {\frac{1}{2\sigma^{v}}\left( {\hat{v} - x} \right)^{2}}}}{{g_{in}^{\prime}\left( {\hat{v},\sigma^{v},q} \right)} = \frac{1}{1 - {\sigma^{v}{\frac{\partial^{2}}{\partial x^{2}}{\log\left\lbrack {p_{x}\left( {x❘q} \right)} \right\rbrack}}}}}{{g_{out}\left( {y,\hat{p},\sigma^{z}} \right)} = \frac{y - \hat{p}}{\sigma^{w} + \sigma^{z}}}{{g_{out}^{\prime}\left( {y,\hat{p},\sigma^{z}} \right)} = {- \frac{1}{\sigma^{w} + \sigma^{z}}}}$ where {circumflex over (v)}, σ^(v), {circumflex over (p)}, σ^(z) are input variables and σ^(w) represents a noise variance; and setting a number of iterations t_(G)=0, a residual ŝ(−1)=0, a sparse vector estimated mean value {circumflex over (x)}_(n) _(s) (t_(G))>0, and a sparse vector estimated variance σ_(n) _(s) ^(x)(t_(G))>0; S33, letting M=N_(c)N_(f)K, where N_(c) represents a number of base stations, K represents a number of code elements, N_(f) represents a number of subcarriers; for m=1,2, . . . , M, calculating estimated mean value {circumflex over (z)}_(m)(t_(G)) and variance σ_(m) ^(z)(t_(G)) of a variable z_(m): ${{\sigma_{m}^{z}\left( t_{G} \right)} = {\sum\limits_{n_{s}}{A_{m,n_{s}}^{2}{\sigma_{n_{s}}^{x}\left( t_{G} \right)}}}}{{{\hat{p}}_{m}\left( t_{G} \right)} = {{\sum\limits_{n_{s}}{A_{m,n_{s}}{{\hat{x}}_{n_{s}}\left( t_{G} \right)}}} - {{\sigma_{m}^{z}(t)}{{\hat{s}}_{m}\left( {t_{G} - 1} \right)}}}}{{{\hat{z}}_{m}\left( t_{G} \right)} = {\sum\limits_{n_{s}}{A_{m,n_{s}}{{\hat{x}}_{n_{s}}\left( t_{G} \right)}}}}$ S34, for m=1,2, . . . , M, calculating a mean value ŝ_(m)(t_(G)) and a variance σ_(m) ^(s)(t_(G)) of the residual as follows: ŝ _(m)(t _(G))=g _(out)(t _(G) , y _(m) , {circumflex over (p)} _(m)(t _(G)), σ_(m) ^(z)(t _(G))) σ_(m) ^(s)(t _(G))=−g′ _(out)(t _(G) , y _(m) , {circumflex over (p)} _(m)(t _(G)), σ_(m) ^(z)(t _(G))) where y_(m) represents an m^(th) element of the receiving signal; S35, for n_(s)=1,2, . . . , N_(s), calculating observed mean value {circumflex over (v)}_(n) _(s) (t_(G)) and variance σ_(n) _(s) ^(v)(t_(G)) of {circumflex over (x)}_(n) _(s) (t_(G)) as follows: ${{{\hat{v}}_{n_{s}}\left( t_{G} \right)} = {{{\hat{x}}_{n_{s}}\left( t_{G} \right)} + {{\sigma_{n_{s}}^{v}\left( t_{G} \right)}{\sum\limits_{m}{A_{m,n_{s}}{{\hat{s}}_{m}\left( t_{G} \right)}}}}}}{{\sigma_{n_{s}}^{v}\left( t_{G} \right)} = \left\lbrack {\sum\limits_{n_{s}}{A_{m,n_{s}}^{2}{\sigma_{n_{s}}^{s}\left( t_{G} \right)}}} \right\rbrack^{- 1}}$ S36, for n_(s)=1,2, . . . , N_(s), calculating observed mean value {circumflex over (x)}_(n) _(s) (t_(G)+1) and variance σ_(n) _(s) ^(x)(t_(G)+1) of x_(n) _(s) : {circumflex over (x)} _(n) _(s) (t _(G)+1)=g _(in)(t _(G) , {circumflex over (v)} _(n) _(s) (t _(G)), σ_(n) _(s) ^(v)(t _(G)), q) σ_(n) _(s) ^(x)(t _(G)+1)=σ_(n) _(s) ^(v)(t _(G))g′ _(in)(t _(G) , {circumflex over (v)} _(n) _(s) (t _(G)), σ_(n) _(s) ^(r)(t _(G)), q) S37, executing steps S33 to S36 repeatedly until a convergence condition Σ_(m)|y_(m)−{circumflex over (z)}_(m)(t_(G))|>ε_(G) is satisfied, where ε_(G) represents an error tolerance; and S38, taking a sparse variable {circumflex over (x)}_(n) _(s) (t_(G)) as a coarse environmental sensing initial result of the environmental information x.
 4. The method according to claim 3, wherein the step S4 comprises the following steps: S41, selecting a predetermined region as a focused region of interest from the whole environment according to the coarse environmental sensing initial result and actual needs, wherein the target object is in the region of interest; S42, in an i^(th) iteration, detecting a background scatterer {circumflex over (x)}_(back) ^((i))(n_(s)) outside the region of interest as follows: ${{\hat{x}}_{back}^{(i)}\left( n_{s} \right)} = \left\{ \begin{matrix} {0,} & {{{\hat{x}}^{(i)}\left( n_{s} \right)} \leq {\gamma_{i}{or}{{\hat{x}}^{(i)}\left( n_{s} \right)}{inside}{{ROI}.}}} \\ {{{\hat{x}}^{(i)}\left( n_{s} \right)},} & {{{\hat{x}}^{(i)}\left( n_{s} \right)} \geq \gamma_{i}} \end{matrix} \right.$ where {circumflex over (x)}^((i))(n_(s)) represents a result in the i^(th) iteration, y_(i) represents a detection threshold of the background scatterer, wherein the detection threshold y_(i) decreases with increase of the number of iterations; and S43, removing a background scattering part from the receiving signal to obtain a receiving signal ŷ_(ROI) ^((i+1)) of the target object in a region of interest (ROI) of an (i+1)^(st) iteration: Ŷ _(ROI) ^((i+1))=(1−a){tilde over (y)}+a(ŷ _(ROI) ^((i)) −Ax _(back) ^((i))) where a represents a weight variable, for enhancing robustness of iterative algorithm, and the weight variable a increases with the increase of the number of iterations.
 5. The method according to claim 1, wherein the step S5 comprises the following steps: S51, setting the prior probability of the environmental information in an iterative focused process, wherein in the i^(th) iteration, assuming that the background scatterer obeys Bernoulli Gaussian distribution, and a prior probability formula p(x_(back)) is expressed as follows: p(x _(back))=(1−λ)δ(x _(back))+λ+(x _(back); θ_(back,i), σ_(back)) where θ_(back,i) and σ_(back) represent a mean value and a variance of a background environmental information distribution, respectively, λ represents a sparse coefficient, N(·) represents a standard normal distribution, and x_(back) represents the background scatterer; wherein scatterer distribution in the selected ROI is a Gaussian distribution, with no sparsity: p(x _(ROI))=

(x _(ROI); θ_(ROI), σ_(ROI)) where θ_(ROI) and σ_(ROI) represent a mean value and a variance of ROI environmental information distribution, respectively; S52, setting, according to the prior probability formula obtained in step S51, the prior probability p(x) of environmental information inside and outside the region of interest in an (i+1)^(st) iteration, wherein x={x_(ROI), x_(back)}; S53, initializing approximate message passing algorithm parameters, and letting input functions g_(in)(·), g′_(in)(·) and output functions g_(out)(·), g′_(out)(·) be as follows: ${{g_{in}\left( {\hat{v},\sigma^{v},q} \right)} = {\arg\max\limits_{x}{F_{in}\left( {x,\hat{v},\sigma^{v},q} \right)}}}{{F_{in}\left( {x,\hat{v},\sigma^{v},q} \right)} = {{\log{p_{x}\left( {x❘q} \right)}} - {\frac{1}{2\sigma^{v}}\left( {\hat{v} - x} \right)^{2}}}}{{g_{in}^{\prime}\left( {\hat{v},\sigma^{v},q} \right)} = \frac{1}{1 - {\sigma^{v}{\frac{\partial^{2}}{\partial x^{2}}{\log\left\lbrack {p_{x}\left( {x❘q} \right)} \right\rbrack}}}}}{{g_{out}\left( {y,\hat{p},\sigma^{z}} \right)} = \frac{y - \hat{p}}{\sigma^{w} + \sigma^{z}}}{{g_{out}^{\prime}\left( {y,\hat{p},\sigma^{z}} \right)} = {- \frac{1}{\sigma^{w} + \sigma^{z}}}}$ letting a number of iterations t_(G)=0, a residual ŝ(−1)=0, a sparse vector estimated mean value {circumflex over (x)}_(n) _(s) (t_(G))>0 and a sparse vector estimate variance σ_(n) _(s) ^(x)(t_(G))>0; S54, letting M=N_(c)N_(f)K, and for m=1,2, . . . , M, calculating an estimated mean value {circumflex over (z)}_(m)(t_(G)) and a variance σ_(m) ^(z)(t_(G)) of z_(m) as follows: ${{\sigma_{m}^{z}\left( t_{G} \right)} = {\sum\limits_{n_{s}}{A_{m,n_{s}}^{2}{\sigma_{n_{s}}^{x}\left( t_{G} \right)}}}}{{{\hat{p}}_{m}\left( t_{G} \right)} = {{\sum\limits_{n_{s}}{A_{m,n_{s}}{{\hat{x}}_{n_{s}}\left( t_{G} \right)}}} - {{\sigma_{m}^{z}(t)}{{\hat{s}}_{m}\left( {t_{G} - 1} \right)}}}}{{{\hat{z}}_{m}\left( t_{G} \right)} = {\sum\limits_{n_{s}}{A_{m,n_{s}}{{\hat{x}}_{n_{s}}\left( t_{G} \right)}}}}$ S55, for m=1,2, . . . , M, calculating a mean value ŝ_(m)(t_(G)) and a variance σ_(m) ^(s)(t_(G)) of the residual as follows: ŝ _(m)(t _(G))=g _(out)(t _(G) , ŷ _(ROI,m) ^(i+1)) ,{circumflex over (p)} _(m)(t _(G)), σ_(m) ^(z)(t _(G))) σ_(m) ^(s)(t _(G))=−g′ _(out)(t _(G) , ŷ _(ROI,m) ^(i+1)) ,{circumflex over (p)} _(m)(t _(G)), σ_(m) ^(z)(t _(G))) where ŷ_(ROI,m) ^(i+1))is an m^(th) element of the receiving signal obtained in S43; S56, for n_(s)=1,2, . . . , N_(s), calculating observed a mean value {circumflex over (v)}_(n) _(s) (t_(G)) and a variance σ_(n) _(s) ^(v)(t_(G)) of {circumflex over (x)}_(n) _(s) (t_(G)) as follows: ${{{\hat{v}}_{n_{s}}\left( t_{G} \right)} = {{{\hat{x}}_{n_{s}}\left( t_{G} \right)} + {{\sigma_{n_{s}}^{v}\left( t_{G} \right)}{\sum\limits_{m}{A_{m,n_{s}}{{\hat{s}}_{m}\left( t_{G} \right)}}}}}}{{{\sigma_{n_{s}}^{v}\left( t_{G} \right)} = \left\lbrack {{\sum}_{n_{s}}A_{m,n_{s}}^{2}{\sigma_{n_{s}}^{s}\left( t_{G} \right)}} \right\rbrack^{- 1}};}$ S57, for n_(s)=1,2, . . . , N_(s), calculating observed mean value {circumflex over (x)}_(n) _(s) (t_(G)+1) and variance σ_(n) _(s) ^(x)(t_(G)+1) as follows: {circumflex over (x)} _(n) _(s) (t _(G)+1)=g _(in)(t _(G) , {circumflex over (v)} _(n) _(s) (t _(G)), σ_(n) _(s) ^(v)(t _(G)), q) σ_(n) _(s) ^(x)(_(G)+1)=σ_(n) _(s) ^(v)(t _(G))g′ _(in)(t _(G) , {circumflex over (v)} _(n) _(s) (t _(G)), σ_(n) _(s) ^(r)(t _(g)), q) S58, repeating steps S54 to S57 until the convergence condition Σ_(m)|y_(m)−{circumflex over (z)}_(m)(t_(G))|>ε_(G) is satisfied; and S59, taking a sparse variable {circumflex over (x)}_(n) _(s) (t_(G)) estimated in the above steps S51 to S58 as a final environment sensing result of a current iteration. 